They endured numerous late finishes and one all-night sitting – but peers finally crossed the finishing line last night in the marathon committee stage debate on plans to reform the voting system and cut the number of MPs.

The government efforts to force the parliamentary voting system and constituencies bill through the House of Lords took 17 days, amid claims of Labour filibustering.

With two stages still to go in the Lords, the bill needs to be returned to the Commons by the end of 14 February in order for a referendum on adopting the alternative vote (AV) for Westminster elections to be held on 5 May.

But for the bill to return to the Commons by its deadline, the normal 14-day interval between committee and report stage will have to be cut.

The bill's remaining amendments were dealt with by 6.51pm yesterday after the opposition finally changed their tactics following an agreement with the government this week.

Labour peers do not oppose the AV referendum, but are against the separate plans included in the bill to reduce the number of MPs from 650 to 600.

Lord Strathclyde, the leader of the Lords, said on Monday that the government would bring forward a "package of concessions" at report stage – the next step in the process.

But despite the thawing of hostilities, the parties have yet to agree a timetable for the remaining stages of the bill, which includes a third reading after the report stage before returning to the Commons, where the bill's passage began.

The former lord chancellor Lord Falconer of Thoroton, who is leading Labour's criticism of the bill, warned on Monday that a deal on the future timing of its progress through the upper house depended on "further agreement on substantive issues between the parties".

And although procedural rules at report stage, which is likely to start on Monday, are stricter than during committee, it would still be possible for Labour peers to attempt to hold up the legislation.

Before Monday's agreement, the government had threatened to attempt to guillotine committee debate before an end to the stand-off was reached.

David Cameron last week met crossbench peers, whose votes would have been crucial if a guillotine were to have succeeded.

The government agreed on Monday the principle of an amendment moved by the crossbench peers' convener, Lady D'Souza, who called for the Boundary Commission to be given some flexibility to hold public inquiries on the constituency changes.